Op, have you made an attempt to print off some info from the gov website to give them a more accurate picture of the vaccine?
Can you remove yourself from considering the impact on yourself and the childcare issues for a little while and instead think about the issue of your PIiL not being vaccinated and focus more in addressing that?
Tatian - are you are anti-vaxxer? What an odd comment to make about the internet! Yes, of course there is lots of odd info on the internet, but it is also a great source if accurate info too. To not have access to a TV or to the internet or radio, means you really are pretty cut off from sources of information, beyond those that come from people who might visit you...and if as OP suggests, some of those give dubious info, it really is a problem.
I wonder if Op’s PiLs are part of an ethnic minority community, who in old age have become very isolated. It sounds like their contacts with the outside world are very restricted and might include some who deliver misinformation. There are more people out there in this kind of position than we might think and they can be very vulnerable to not knowing what is going on or not being able to make properly informed choices.
I think Op’s real concern in the short term is to correct that lack of information. Essentially it could save their lives. And that is probably more important really than the childcare issues.
If once they have proper info they still decide not to be vaccinated, having fully understood the risks this gives them and consequences for going out etc, then Op can consider childcare, shopping etc.
It is fine to make whatever choice you want.... yet I would like to think people can make an informed choice,